Polytopes and graphs:
This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY
Cambridge University Press
2024
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
211 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-634 DE-92 URL des Erstveröffentlichers |
| Zusammenfassung: | This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 14 Mar 2024) |
| Beschreibung: | 1 Online-Ressource (xiii, 465 Seiten) |
| ISBN: | 9781009257794 |
| DOI: | 10.1017/9781009257794 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV049778330 | ||
| 003 | DE-604 | ||
| 005 | 20240719 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 240712s2024 |||| o||u| ||||||eng d | ||
| 020 | |a 9781009257794 |c Online |9 978-1-009-25779-4 | ||
| 024 | 7 | |a 10.1017/9781009257794 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781009257794 | ||
| 035 | |a (OCoLC)1446259203 | ||
| 035 | |a (DE-599)BVBBV049778330 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-634 | ||
| 082 | 0 | |a 516/.158 | |
| 100 | 1 | |a Pineda Villavicencio, Guillermo |e Verfasser |0 (DE-588)1330338863 |4 aut | |
| 245 | 1 | 0 | |a Polytopes and graphs |c Guillermo Pineda Villavicencio |
| 264 | 1 | |a Cambridge, United Kingdom ; New York, NY |b Cambridge University Press |c 2024 | |
| 300 | |a 1 Online-Ressource (xiii, 465 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge studies in advanced mathematics |v 211 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 14 Mar 2024) | ||
| 520 | |a This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field | ||
| 650 | 4 | |a Convex polytopes | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Hardcover |z 9781009257817 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 9781009257770 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781009257794?locatt=mode:legacy |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035119350 | |
| 966 | e | |u https://doi.org/10.1017/9781009257794?locatt=mode:legacy |l DE-12 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781009257794?locatt=mode:legacy |l DE-634 |p ZDB-20-CBO |q BTU_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781009257794?locatt=mode:legacy |l DE-92 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1806142701039517696 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Pineda Villavicencio, Guillermo |
| author_GND | (DE-588)1330338863 |
| author_facet | Pineda Villavicencio, Guillermo |
| author_role | aut |
| author_sort | Pineda Villavicencio, Guillermo |
| author_variant | v g p vg vgp |
| building | Verbundindex |
| bvnumber | BV049778330 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781009257794 (OCoLC)1446259203 (DE-599)BVBBV049778330 |
| dewey-full | 516/.158 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.158 |
| dewey-search | 516/.158 |
| dewey-sort | 3516 3158 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781009257794 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nmm a2200000zcb4500</leader><controlfield tag="001">BV049778330</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240719</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">240712s2024 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781009257794</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-009-25779-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781009257794</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781009257794</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1446259203</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049778330</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.158</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pineda Villavicencio, Guillermo</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1330338863</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Polytopes and graphs</subfield><subfield code="c">Guillermo Pineda Villavicencio</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge, United Kingdom ; New York, NY</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2024</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiii, 465 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">211</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 14 Mar 2024)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex polytopes</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Hardcover</subfield><subfield code="z">9781009257817</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">9781009257770</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781009257794?locatt=mode:legacy</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035119350</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781009257794?locatt=mode:legacy</subfield><subfield code="l">DE-12</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781009257794?locatt=mode:legacy</subfield><subfield code="l">DE-634</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BTU_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781009257794?locatt=mode:legacy</subfield><subfield code="l">DE-92</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV049778330 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-01T00:25:05Z |
| institution | BVB |
| isbn | 9781009257794 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035119350 |
| oclc_num | 1446259203 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-634 |
| owner_facet | DE-12 DE-92 DE-634 |
| physical | 1 Online-Ressource (xiii, 465 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO BTU_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Pineda Villavicencio, Guillermo Verfasser (DE-588)1330338863 aut Polytopes and graphs Guillermo Pineda Villavicencio Cambridge, United Kingdom ; New York, NY Cambridge University Press 2024 1 Online-Ressource (xiii, 465 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 211 Title from publisher's bibliographic system (viewed on 14 Mar 2024) This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field Convex polytopes Erscheint auch als Druck-Ausgabe, Hardcover 9781009257817 Erscheint auch als Druck-Ausgabe, Paperback 9781009257770 https://doi.org/10.1017/9781009257794?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Pineda Villavicencio, Guillermo Polytopes and graphs Convex polytopes |
| title | Polytopes and graphs |
| title_auth | Polytopes and graphs |
| title_exact_search | Polytopes and graphs |
| title_full | Polytopes and graphs Guillermo Pineda Villavicencio |
| title_fullStr | Polytopes and graphs Guillermo Pineda Villavicencio |
| title_full_unstemmed | Polytopes and graphs Guillermo Pineda Villavicencio |
| title_short | Polytopes and graphs |
| title_sort | polytopes and graphs |
| topic | Convex polytopes |
| topic_facet | Convex polytopes |
| url | https://doi.org/10.1017/9781009257794?locatt=mode:legacy |
| work_keys_str_mv | AT pinedavillavicencioguillermo polytopesandgraphs |